Verifying breaker rating of AM-14

He is correct. I'll not go into the particulars but the fact is, you have two separate circuits connected to the same breaker. Separate the two circuits by installing another 15-Amp breaker. Although I understand your situation, please understand wire gauge and electrical amperage are two different animals. Breakers are rated in Amperage and electrical conductors are sized by wire gauge. That said, the 20 gauge wire you speak of is actually a 12 gauge conductor and the 15 gauge wire as you say is a 14 gauge conductor. Have a good day.

13Mb product manual is a big download ... electrical info page 13:
http://waterheatertimer.org/pdf/AO-Smith-Cyclone-gas-water-heater.pdf
http://waterheatertimer.org/pdf/AO-Smith-Cyclone-electrical-connection.pdf
Recommended both water heaters require dedicated single-phase 15 amp 120Volt line with correct polarity. This is 14 gauge wire and 15 amp breaker for each unit.
I would put both water heaters on surge protection and GFCI. Most water heaters are not protected from surge, and manual says line noise can affect operation of water heater.
Your local code would say if GFCI is required. Install GFCI breaker in main panel if required.
Install inline surge protector: Or add main breaker box protection.
http://www.amazon.com/dp/B003AU0Z48/?tag=waterheaterti-20

AO Smith service handbooks:
http://www.hotwater.com/resources/product-literature/service-handbooks/
Add a comment and say what you discover

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Following wiring diagram is for general purpose household 120V-240Volt service.
http://waterheatertimer.org/images/Inside-Main-Breaker-Box-10-1000.jpg
http://waterheatertimer.org/See-inside-main-breaker-box.html
http://waterheatertimer.org/Color-codewire.html

Why are you asking that question without saying what you are wiring? 120Volt, 277V, 480V etc?
What does rating plate say on device you are connected to 14-3 wire?
And what amp/volt/watt rating are you connecting to 14 gauge wire?
No electrician would omit that information.
14-3 wire is usually only for 3-way switches and other light duty applications.
Must be connected to 15 amp breaker and no larger.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Look at rating plate on side of unit for Volts, Amps, Watts.
Volts x amps = watts.
If unit is 240Volts, then you need double-pole 240Volt breaker
If unit is 8500 watts at max power, then 8500 watts divided by 240Volts = 35 amps.

What size breaker for 35 amps?
When electricians figure load rating for breakers, they use the 80% rule.
40 amp breaker x 80% = 32 amp safe maximum load for 40 amp breaker. Use 8 gauge wire with 40 amp breaker.
50 amp breaker x 80% = 40 amp safe maximum for 50 amp breaker. I use 6 gauge wire with 50 amp breaker.
60 amp breaker x 80% = 48 amp safe maximum for 60 amp breaker. Again, use 6 gauge wire with 60 amp breaker.

How to connect wires to unit.
First of all, all outdoor HVAC units require power cut off located next to unit.
This lets the mechanic, or service tech turn power off to work on unit, even if the mechanic does not have access to main breaker box.

Next, open unit to see where wires connect.
If unit has wires, then connect both hot wires from 240 breaker to the wires inside unit. Connect bare ground wire to green ground screw.
If unit has terminals. The terminals will be labeled L1 L2. Connect each hot wire from 240Volt breaker to either one of the screw terminals. Then bare ground goes to green ground screw.

Copy following links for basic illustrations connecting wires to terminals, and to breakers, and selecting wire size.
http://waterheatertimer.org/How-to-wire-Tankless-electric-water-heater.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

The water heater has two 4500 watt elements.
However both elements are not turned-ON at same time
So the water heater is 4500 Watts

Volts x Amps = watts
Amps =watts divided by volts
Amps = 4500 Watts divided by 240 Volts
Amps= 18.75

So that says a 20 amp breaker ... except for the 80% rule
80% rules says for safety, your Amp rating should be multiplied by 80%

20 amp breaker X 80% = 16 amps
20 amp breaker is actually safe for just 16 amps, and your water heater draws 18.75 amps.

The calculation shows you need a 30 Amp breaker.
30 Amp breaker requires 10 gauge wire.

http://waterheatertimer.org/Figure-Volts-Amps-Watts-for-water-heater.html

Most likely not.Heating equipment circuit breakers have to be calculated at 100% of the load continuous. That would mean the circuit breaker would have to be rated at 45amps continuous. Most breakers are not. Most breakers are rated at 80% of their rating for continuous loads. So if you installed a 60 amp circuit, 80% of 60 = 48 amps. This would fit your requirement. That would be a 60amp breaker, with #6 cu conductors.

Generally NO as UK uses a different line value than US (SECAM )VS (NTSC) also the power ratings are different 240V as oposed to 120V for USA

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For about $20.00 you can buy 50 feet of 12 guage 3 wire yellow extention cord. You will then get all the amps you need to run your unit. If it still fails, you have a problem inside the tiller.
Tom MN

WITHOUT ANYTHING TO LOOK AT I WOULD SAY HE CONNECTED HALF THE LOAD TO ONE OF THE PHASE WIRES AND THE OTHER TO THE OTHER PHASE WIRES , PHASE WIRES MEANING 120/240 SINGLE PHASE , SO IF THAT IS THE CASE TAKE THE WIRES HE HAS BUNDLED TO ONE PHASE OR ONE TERMINAL ON THE BREAKER AND THE OTHER TO THE OTHER TERMINAL OF THE BREAKER IN SOME CASES IT IS NECESSARY TO CONNECT THE WIRES WITH CONNECTOR, APPROVED TYPE AND THEN TO THE BREAKER TERMINAL ,THIS JUMPER SHOULD BE RATED THE RATEDING OF THE BREAKER YOU ARE INSTALLING ,GOOD LUCK